Simplify the complex fraction by flipping the denominator and multiplying it by the numerator. Then reduce the result. Replace the first fraction by using the ratio identity for tangent and the second fraction by using the reciprocal identity for cosecant.
How do you simplify expressions?
To simplify any algebraic expression, the following are the basic rules and steps:
- Remove any grouping symbol such as brackets and parentheses by multiplying factors.
- Use the exponent rule to remove grouping if the terms are containing exponents.
- Combine the like terms by addition or subtraction.
- Combine the constants.
How can you determine if an expression is already simplified?
A rational expression is reduced to lowest terms if the numerator and denominator have no factors in common.
How do you factor trigonometric identities?
When to Factor a Trigonometry Identity
- Factor sin x out of each term in the numerator.
- Replace the expression in the parentheses with its equivalent by using the Pythagorean identity.
- Now split up the fraction into a product of two fractions, carefully arranging the numerator and denominator.
Can you separate denominators?
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.